International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 8, Pages 453-458
One-sided complements and solutions of the equation in semirings
1Lipetsk State Technical University, Lipetsk 398055, Russia
2Department of Mathematics, University of Haifa, Haifa 31905, Israel
Received 22 July 2001
Copyright © 2002 Sam L. Blyumin and Jonathan S. Golan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Given multiplicatively-regular elements and in a semiring
, and given an element of , we find a complete set of solutions to the equation . This result is then extended to equations over matrix semirings.